{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "421f1765",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "# -----------------------------------------------------------------------------\n",
    "# Author: Zexiong Wu, Xueyou Li (wuzx58@mail2.sysu.edu.cn, lixueyou@mail.sysu.edu.cn)\n",
    "# Date: 2024-06-09\n",
    "# Description: Load PINN model\n",
    "# Article: https://link.cnki.net/urlid/32.1124.TU.20250926.1432.002\n",
    "# -----------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "25d200c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Custom neural network\n",
    "class CustomNetwork(nn.Module):\n",
    "    def __init__(self, layers, activation=nn.Tanh(), is_TanhShrink=False):\n",
    "        super().__init__()\n",
    "        activation_list = [activation] * (len(layers) - 2)\n",
    "        if is_TanhShrink:\n",
    "            activation_list[0] = nn.Tanhshrink()\n",
    "            activation_list[-1] = nn.Tanhshrink()\n",
    "        self.networks = self.create_network(layers, activation_list)\n",
    "\n",
    "    # Build the sequential network\n",
    "    def create_network(self, layers, activation_list):\n",
    "        network = nn.Sequential()\n",
    "        for i in range(len(layers)-2):\n",
    "            network.add_module('linear{}'.format(i+1), nn.Linear(layers[i], layers[i+1]))\n",
    "            network.add_module('activation{}'.format(i+1), activation_list[i])\n",
    "        network.add_module('output', nn.Linear(layers[-2], layers[-1]))\n",
    "        return network\n",
    "    \n",
    "    # Forward pass with hard constraint\n",
    "    def forward(self, inputs_list):\n",
    "        xN, LpN, MtN, VtN = inputs_list\n",
    "        inputs_tensor = torch.cat(inputs_list, dim=1)\n",
    "        outputs_tensor = self.networks(inputs_tensor)\n",
    "        y = outputs_tensor[:, 0].unsqueeze(1) * MtN + outputs_tensor[:, 1].unsqueeze(1) * VtN\n",
    "        return y\n",
    "    \n",
    "    # Output all required physical quantities\n",
    "    def outputs(self, input_list):\n",
    "        '''input_list: [x, Mt, Vt, EI, Lp, m, b0]'''\n",
    "        x, Mt, Vt, EI, Lp, m, b0 = input_list\n",
    "        alpha = (m * b0 / EI)**(1 / 5)\n",
    "        xN = x * alpha\n",
    "        LpN = Lp * alpha\n",
    "        VtN = Vt / (EI * alpha**3)\n",
    "        MtN = Mt / (EI * alpha**2)\n",
    "        y = self.forward([xN, LpN, MtN, VtN])\n",
    "        dy = gradients(y, x, 1)\n",
    "        d2y = gradients(dy, x, 1)\n",
    "        d3y = gradients(d2y, x, 1)\n",
    "        d4y = gradients(d3y, x, 1)\n",
    "        return [y, dy, d2y*EI, d3y*EI, d4y*EI]\n",
    "\n",
    "# Compute gradients of u with respect to x\n",
    "def gradients(u, x, order=1):\n",
    "    if order == 1:\n",
    "        return torch.autograd.grad(u, x, grad_outputs=torch.ones_like(u),\n",
    "                                   create_graph=True,\n",
    "                                   retain_graph=True,\n",
    "                                   only_inputs=True,)[0]\n",
    "    else:\n",
    "        return gradients(gradients(u, x), x, order=order - 1)\n",
    "\n",
    "# Mean squared error\n",
    "def MS(equ):\n",
    "    return torch.mean(equ**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0d315ee9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load model\n",
    "def load_model(filename):\n",
    "    model = CustomNetwork(layers=[4] + [50] * 4 + [2], activation=nn.Tanh(), is_TanhShrink=True)\n",
    "    model.load_state_dict(torch.load(filename + '.pth'))\n",
    "    model.eval()\n",
    "    return model\n",
    "model = load_model('PINN_m_method_pile')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2a4e9343",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Predict\n",
    "Lp = 15\n",
    "E = 2.8e7\n",
    "Vt = 60\n",
    "Mt = 700\n",
    "D = 1.5\n",
    "b0 = 2.25\n",
    "m = 9400\n",
    "\n",
    "EI = E * (np.pi * D**4) / 64\n",
    "model.to('cpu')\n",
    "x = torch.linspace(0, Lp, 100).view(-1, 1).requires_grad_(True)\n",
    "input_list = [x, Mt*torch.ones_like(x), Vt*torch.ones_like(x), EI*torch.ones_like(x),\n",
    "              Lp*torch.ones_like(x), m*torch.ones_like(x), b0*torch.ones_like(x)]\n",
    "output_list = model.outputs(input_list)\n",
    "\n",
    "plt.figure(figsize=(15, 3))\n",
    "for i in range(5):\n",
    "    plt.subplot(1, 5, i+1)\n",
    "    plt.plot(output_list[i].detach().numpy(), x.detach().numpy())\n",
    "    plt.gca().invert_yaxis()\n",
    "    plt.ylabel('x')\n",
    "    plt.xlabel(['y', '$\\Theta$', '$M$', '$F_s$', '$p$'][i])\n",
    "    plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40946359",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py38",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
